Advanced Markov Chain Monte Carlo Methods: Learning from Past Samples

An actively pursued research direction for alleviating the local‐trap problem suffered by the Metropolis‐Hastings (MH) algorithm is the population‐based MCMC, where a population of Markov chains are run in parallel, each equipped with possibly different but related invariant distributions. This chapter describes the different ways of specifying the trial distributions and updating the population of Markov chains lead to different algorithms, such as adaptive direction sampling, conjugate gradient Monte Carlo, parallel tempering, evolutionary Monte Carlo, sequential parallel tempering, and equi‐energy sampler. The chapter then considers three applications of the evolutionary Monte Carlo (EMC) algorithm, including Bayesian curve fitting, protein folding simulations, and nonlinear time series forecasting.

Controlled Vocabulary Terms

Metropolis‐Hastings Algorithm